Dynamics of Water Entry

The hydrodynamics associated with water-entry of spheres can be highly variable with respect to the material and kinematic properties of the sphere. This series of five fluid dynamics videos illustrates several subtle but interesting variations. The first series of videos contrasts the nature of impact between a hydrophilic and hydrophobic sphere, and illustrates how surface coating can affect whether or not an air cavity is formed. The second video series illustrates how spin and surface treatments can alter the splash and cavity formation following water entry. The spinning sphere causes a wedge of fluid to be drawn into the cavity due to the no-slip condition and follows a curved trajectory. The non-spinning sphere has two distinct surface treatments on the left and right hemispheres: the left hemisphere is hydrophobic and the right hemisphere is hydrophilic . Interestingly, the cavity formation for the half-and-half sphere has many similarities to that of the spinning sphere especially when viewed from above. The third video series compares two millimetric nylon spheres impacting at slightly different impact speeds (Uo = 40 and 45 cm/s); the faster sphere fully penetrates the free surface, forming a cavity, whereas the slower sphere does not. The fourth series shows the instability of an elongated water-entry cavity formed by a millimetric steel sphere with a hydrophobic coating impacting at Uo = 600 cm/s. The elongated cavity forms multiple pinch-off points along its decent. Finally, a millimetric steel sphere with a hydrophobic coating breaks the free surface with an impact speed of Uo = 350 cm/s. The cavity pinches-off below the surface, generating a Worthington jet that pinches into droplets owing to the Rayleigh-Plateau instability.Comment: American Physical Society Division of Fluid Dynamics Gallery of Fluid Motion Video Entry Replaced previous version because abstract had LaTex markup and was too lon

Quantitative Flow Field Imaging about a Hydrophobic Sphere Impacting on a Free Surface

This fluid dynamics video shows the impact of a hydrophobic sphere impacting a water surface. The sphere has a mass ratio of m* = 1.15, a wetting angle of 110 degrees, a diameter of 9.5 mm, and impacts the surface with a Froude number of Fr = 9.2. The first sequence shows an impact of a sphere on the free surface illustrating the formation of the splash crown and air cavity. The cavity grows both in the axial and radial direction until it eventually collapses at a point roughly half of the distance from the free surface to the sphere, which is known as the pinch-off point. The second set of videos shows a sphere impacting the free surface under the same conditions using Particle Image Velocimetry (PIV) to quantify the flow field. A laser sheet illuminates the mid-plane of the sphere, and the fluid is seeded with particles whose motion is captured by a high-speed video camera. Velocity fields are then calculated from the images. The video sequences from left to right depict the radial velocity, the axial velocity, and the vorticity respectively in the flow field. The color bar on the far left indicates the magnitude of the velocity and vorticity. All videos were taken at 2610 fps and the PIV data was processed using a 16 x 16 window with a 50% overlap.Comment: American Physical Society Division of Fluid Dynamics 2008 Annual Meeting Replaced previous version because abstract had LaTex markup and was too long, missing periods on middle initial of first two name

Cavity dynamics of water entry for spheres and ballistic projectiles

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Includes bibliographical references.The free surface impact of solid objects has been investigated for well over a century. This canonical problem has many facets that may be studied: object geometry, surface treatment, and diameter; impact speed and angle; and fluid viscosity and surface tension. The problem is further enriched with the consideration of varying mass ratios and rotational velocities. This thesis uses advanced high-speed imaging and visualization techniques to discover underlying physics and further our understanding of these phenomena through improvements to analytical solutions describing criterion such as cavity formation, depth of deep seal, and trajectory for all impact parameters studied. The topic is extended to the impact of high-speed projectiles or bullets. Through experimentation the trajectory, cavity size, and forces acting on the projectiles are elucidated. Experimentation coupled with improvements to an existing cavitation model lead to an improved bullet design that forms a narrower cavity and achieves higher speeds. Industrial applications include ship slamming, extreme waves and weather on oil platforms, sprayed adhesives, paint aerosols and ink jet printing. In the field of naval hydrodynamics there is particular interest as these problems relate to the study of the water entry of mines and bullets, and the underwater launching of torpedos and missiles. Physical insight can also be applied to sports performance research relating to the water entry of athletes, reducing drag of swimmers near the free surface, decreasing cavity formation for divers, and the entry and exit of oars in rowing.(cont.) This thesis examines the effect of several key parameters on the water entry physics of spheres at relatively low Froude numbers including: hydrophobic vs. hydrophilic surfaces, mass ratio and rotational velocity. Physical models that predict the depth of deep seal and the effect of dynamic and static wetting angle on cavity formation will be discussed. Theories are derived from physical parameters witnessed through high-speed video image sequences using advanced image processing techniques. New phenomena have been witnessed via these techniques including a wedge of fluid that crosses the cavity in the case of transverse rotational velocity. Furthermore, the images reveal the forces acting on the sphere through the entire trajectory, which adds valuable information for future theoretical models. The discussion continues with the water entry of bullets, which produce water vapor cavities large enough to engulf the projectile (i.e. supercavitation). The effects of speed, geometry and angle of attack on the formation of the subsurface cavity are analyzed through an improved physical model and full scale experimentation. The analytical model is then used to improve the design of projectile geometry to allow for more efficient travel inside the cavity and experimentally validated.by Tadd Trevor Truscott.Ph.D

Error sources in three-dimensional microscopic light field particle image velocimetry

Three-dimensional (3D) microscopic velocimetry methods have been increasingly developed in recent years to meet the measurement demands of microfluidic systems. As all 3D microscopic velocimetry techniques involve reconstructing a volume from two-dimensional (2D) sensor(s), sources of uncertainty arise that are unique from 2D velocimetry methods. This study discusses the error sources associated with a recently developed microscopic light field particle image velocimetry (LFPIV) method. The LFPIV technique combines altered optical hardware with postcapture computation to reconstruct 3D volumes. A microlens array placed at the intermediate image plane of an infinity corrected objective captures the directionality of light rays, which may then be reparameterized to form a 3D focal stack. The error sources of LFPIV are typical of image-based 3D reconstruction. We group these errors into four categories: experimental setup, calibration, 3D reconstruction, and velocimetry. All 3D microscopic particle image velocimetry methods introduce additional complexity into the experimental setup and the particular challenges of LFPIV will be highlighted. Calibration errors arise from imperfect mapping between the 3D world and LFPIV instrument (optics and computation inclusive). The most unique error source in 3D velocimetry methods stems from 3D reconstruction. Objects are typically estimated with large error on the depth dimension. We discuss the magnitude of this error for LFPIV and its dependency on instrument design. Methods for improving reconstruction quality, such as 3D deconvolution and focus-based thresholding, are assessed. Most importantly, the impact of these error sources on uncertainty, accuracy, and resolution of velocity measurements is quantified using data from a microchannel flow field, a numerical model and simulated data. Comparisons to existing techniques are made whenever possible

Drop on a Bent Fibre

Inspired by the huge droplets attached on cypress tree leaf tips after rain, we find that a bent fibre can hold significantly more water in the corner than a horizontally placed fibre (typically up to three times or more). The maximum volume of the liquid that can be trapped is remarkably affected by the bending angle of the fibre and surface tension of the liquid. We experimentally find the optimal included angle ($\sim {36}{^\circ}$) that holds the most water. Analytical and semi-empirical models are developed to explain these counter-intuitive experimental observations and predict the optimal angle. The data and models could be useful for designing microfluidic and fog harvesting devices

On the Threshold of Drop Fragmentation under Impulsive Acceleration

We examine the complete landscape of parameters which affect secondary breakup of a Newtonian droplet under impulsive acceleration. A Buckingham-Pi analysis reveals that the critical Weber number $\mathit{We}_\mathit{cr}$ for a non-vibrational breakup depends on the density ratio $(\rho)$, the drop $(\mathit{Oh}_d)$ and the ambient $(\mathit{Oh}_o)$ Ohnesorge numbers. Volume of fluid (VOF) multiphase flow simulations are performed using Basilisk to conduct a reasonably complete parametric sweep of the non-dimensional parameters involved. It is found that, contrary to current consensus, even for $\mathit{Oh}_d \leq 0.1$, a decrease in $\mathit{Oh}_d$ has a substantial impact on the breakup morphology, motivating plume formation. In addition to $\rho$, $\mathit{Oh}_o$ also affects the balance between pressure differences between a droplet's pole and its periphery, and the shear stresses on its upstream surface, which ultimately dictates the flow inside the droplet. This behavior manifests in simulations through the observed pancake shapes and ultimately the breakup morphology (forward or backward bag). All these factors affecting droplet deformation process are specified and theories explaining the observed results are provided. A $\mathit{We}_\mathit{cr}-\mathit{Oh}_d$ plot is provided to summarize all variations in $\mathit{We}_\mathit{cr}$ observed due to changes in the involved non-dimensional parameters. All observed critical pancake and breakup morphologies are summarized using a phase diagram illustrating all deformation paths a droplet might take under impulsive acceleration. Finally, based on the understanding of process of bag breakup gained from this work, a non-dimensional parameter to predict droplet breakup threshold is derived and tested on all simulation data obtained from this work and all experimental data gathered from existing literature